Medical physics and astronomy (A Level)

24. Medical Physics

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24. Medical Physics — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Explain how ultrasound, X-rays, CT scans and PET scans are produced, used and compared, and use acoustic impedance, attenuation and annihilation.Transducer = an…

Piezoelectric effect
Applications
Transducer structure
Transmit and receive
Imaging process
Acoustic impedance Z

Section 1 of 10The piezoelectric effect and transducers

Transducer = any device that converts energy from one form to another.
Piezoelectric effect = certain crystals (such as quartz, a lattice of silicon dioxide) produce a p.d. when deformed,
- and deform when a p.d. is applied.
- Compressing or stretching the crystal induces an e.m.f., and alternating compression gives an alternating e.m.f.
- An alternating p.d. makes the crystal vibrate at the same frequency, producing sound.
- The crystal is cut to a size that resonates at the required frequency.
Applications
- microphones and ultrasound transmitters and receivers.
  - (pressure variations to electrical signals)

Section 2 of 10Generating and using ultrasound

Ultrasound = sound with a frequency above the range of human hearing (above 20 kHz), typically in the MHz range for medical use.
Transducer structure
- a piezoelectric crystal with electrodes supplying an alternating p.d.
Damping
- the crystal is backed with epoxy resin so it gives short pulses, which improves resolution.
Transmit and receive
- the same crystal acts as transmitter (p.d. to sound) and receiver.
  - (sound to alternating p.d.)
Imaging process
- the transducer sends a pulse into the body, which is partly reflected at boundaries between tissues.
- The echo returns and generates an electrical signal for the scanner.
- The scanner uses the speed of sound and the time delay to calculate depth, and the echo intensity to show the nature of the boundary.
- Many pulses are combined into a two-dimensional image, as for an unborn child.
Frequency
- a higher frequency gives a shorter wavelength and better resolution, so smaller details are seen.

Section 3 of 10Acoustic impedance and coupling gel

Acoustic impedance Z = the product of the density of a medium and the speed of ultrasound in it, Z = ρc, in kg m⁻² s⁻¹.
- Sound is fastest in solids and slowest in gases, because closer particles pass vibrations faster.
- The c is the speed of sound, not light.
Boundary behaviour
- part of the wave is reflected and part transmitted, and a larger difference in impedance gives greater reflection.
Intensity reflection coefficient
- α = I_R/I₀ = (Z₂ − Z₁)²/(Z₂ + Z₁)², given in the data booklet.
- If Z₁ = Z₂ there is no reflection.
- Energy is conserved, I₀ = I_T + I_R.
Problem
- air has Z about 400 kg m⁻² s⁻¹ and skin about 1.7 × 10⁶, so almost all ultrasound reflects at an air gap (α ≈ 1).
Coupling gel
- a gel with impedance similar to skin fills the gap, so very little is reflected (α ≈ 0.001) and most of the beam enters the body.
- It matches impedances and does not make the ultrasound travel faster.

Section 4 of 10Attenuation of ultrasound

Attenuation = the loss of intensity as a wave is absorbed while travelling through a material.
Equation
- I = I₀e^−μx, where μ is the absorption coefficient (m⁻¹) and x the distance; this equation is not given.
Frequency dependence
- about 0.5 dB cm⁻¹ is lost for every 1 MHz of frequency.
Image formation
- attenuation is not a major problem, because the image is made from reflections at boundaries.
Echoes from depth
- the beam is attenuated going in, partly reflected and attenuated coming back, so the path is 2x.

Section 5 of 10Producing X-rays

X-rays = short-wavelength electromagnetic radiation, about 10⁻⁸ to 10⁻¹³ m.
Production
- electrons from a heated cathode are accelerated to a metal anode target.
  - (thermionic emission)
- The fast electrons decelerate in the target, transferring kinetic energy to X-ray photons.
- Electrons in the target atoms dropping to lower energy levels release characteristic X-ray photons.
Maximum photon energy
- E_max = eV = hf_max = hc/λ_min.
Spectrum
- continuous,
- because electrons decelerate by different amounts, with a sharp cut-off at short wavelength because each electron gives its energy to at most one photon.

Section 6 of 10Quality of X-ray images and attenuation

Aim
- minimise the patient's exposure and maximise the contrast and sharpness of the image.
Exposure
- X-rays are ionising and can damage tissue or cause cancer.
- An aluminium filter absorbs long-wavelength (soft) X-rays, which are absorbed by the body and do not form the image.
Contrast = the difference in blackening between structures.
- It improves with hard X-rays for bone, softer X-rays for tissue and a contrast medium.
- Good contrast needs a large difference between the transmitted intensities through different structures.
Sharpness = how well-defined edges are, improved by a narrower beam, a collimator or lead grid to cut scattering, and smaller pixels.
Attenuation
- bone absorbs X-rays strongly, so it appears white.
- I = I₀e^−μx, where μ is the linear absorption coefficient and depends on photon energy and material.
- Half-value thickness is the thickness of material that halves the beam intensity.
- For several materials multiply the factors, I/I₀ = e^−μ₁x₁ × e^−μ₂x₂.

Section 7 of 10CT scanning

CT (CAT) scan = an X-ray tube rotates around a stationary patient, taking images of one slice from many angles,
- and a computer combines successive slices into a 3D image that can be viewed from any angle.

Advantages	Disadvantages
Higher resolution than a single X-ray	Much higher radiation dose
Distinguishes tissues with similar attenuation coefficients	Possible side effects from contrast media
Produces a 3D image

Dose
- a CT scan needs many exposures from many angles, whereas a plain X-ray needs one.

Section 8 of 10Radioactive tracers

Tracer = a substance containing radioactive nuclei, introduced to the body and absorbed by tissue to study the structure and function of organs.
Suitable isotopes
- technetium-99m and fluorine-18 bind to organic molecules, emit gamma or positron radiation and decay to stable isotopes.
  - (such as glucose)
- Technetium-99m has a half-life of 6 hours.
- Fluorine-18 has a half-life of 110 minutes, so exposure is short.
Uses
- diagnosing cancer, finding areas of reduced blood flow in the heart, and detecting brain injury, Alzheimer's disease and dementia.
Monitoring
- the tracer appears on the screen once tissues absorb it, showing the progress of a disease and the effect of treatment.

Section 9 of 10PET scanning and annihilation

PET (positron emission tomography) = imaging of tissue by measuring the metabolic activity of cells, commonly using fluorodeoxyglucose (glucose containing fluorine-18).
Decay
- fluorine-18 undergoes β⁺ decay: ¹⁸₉F → ¹⁸₈O + ⁰₊₁e + ν_e.
Annihilation
- a positron travels less than a millimetre, meets an electron and both are destroyed, converting their mass to energy as two gamma photons in opposite directions.
- Mass, energy and momentum are conserved, and any particle and its antiparticle can annihilate.
- Each photon has E = hf = m_ec² and momentum p = E/c.

Section 10 of 10Detecting gamma rays in PET

Scanner
- the patient lies in a ring of detectors, each with a scintillator crystal and a photomultiplier.
- A gamma photon excites electrons in the crystal, which excite others, and as they return to lower states they emit faint visible light.
- The photomultiplier amplifies the light and converts it to an electrical signal.
Line of response
- the two photons travel in opposite directions, so a pair of simultaneous hits defines a line through the annihilation point.
Image
- a computer processes many lines and arrival times, and more photons from a point mean more tracer there, which appears as a bright area.
Practical points
- the short half-life gives low exposure but the patient must be scanned quickly, and PET scanners are expensive and not in every hospital.

Last updated: 14 October 2026